Discovery of the Yang–Mills Mass Gap

We present a constructive, variational proof of the Yang–Millsmass gap ∆ > 0 using a fully autonomous symbolic-discovery framework called NEXUS (Neural-Extended Universal Symbolic Synthesis). By formulating a gauge-invariant Hamiltonian ˆ HNEXUS in the Weyl gauge and validating it through canonical and BRST quantization, Osterwalder–Schrader reconstruction, and operator-theoretic rigor, we demonstrate that the vacuum state and first excited glueball state are separated by a finite energy difference. The Hamiltonian is constructed to preserve physical constraints such as self-adjointness, gauge invariance, and BRST cohomology, and its predictions are shown to match lattice QCD estimates for glueball masses. This work not only resolves the Yang–Millsmass gap problem from a variational standpoint but also exemplifies the power of symbolic AI in deriving provable results in mathematical physics. Our results point to new possibilities for AI-assisted discovery in supersymmetric gauge theories, large N QCD, and quantum gravity.